摘要:

A new class of simple tests is proposed for the general multivariate two-sample problem based on the (possibly weighted) proportion of allknearest neighbor comparisons in which observations and their neighbors belong to the same sample. Large values of the test statistics give evidence against the hypothesisHof equality of the two underlying distributions. Asymptotic null distributions are explicitly determined and shown to involve certain nearest neighbor interaction probabilities. Simple infinite-dimensional approximations are supplied. The unweighted version yields a distribution-free test that is consistent against all alternatives; optimally weighted statistics are also obtained and asymptotic efficiencies are calculated. Each of the tests considered is easily adapted to a permutation procedure that conditions on the pooled sample. Power performance for finite sample sizes is assessed in simulations.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478337

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A specimen can have two or more important strength properties. These could be its bending strength and tensile strength. Assuming joint normality, we study experimental designs for estimating the correlation coefficient. The specimen is proof loaded—say, in bending. If it does not fail, it is loaded in tension to failure. Optimal proof loads are determined. Large sample properties of the maximum likelihood estimator are also given.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478338

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Single replicate factorial designs for incomplete block experiments are obtained by first constructing a single replicatepreliminary designin incomplete blocks for the same number of factors but an excessive number of levels of the first factor, then deleting the excess treatment combinations to obtain adeletion design.Any single replicate preliminary design yields a single replicate deletion design. Furthermore, if the preliminary design is orthogonal, then the resulting deletion design is shown to be nearly orthogonal and, under certain reduced models, to provide efficient estimation of lower-order effects and in some cases an orthogonal analysis. For example, a 2×32deletion design is constructed in three blocks of size 6, the 2 df confounded being the sum of interaction effects ofF2andF3and second-order interaction effects. If second-order interactions are assumed negligible, then the deletion design provides efficient estimation of interactions betweenF2andF3and an orthogonal analysis. In another example, a 2×32deletion design is constructed in nine blocks of size 2 with main effects ofF1unconfounded. In a main-effects model, main effects ofF2andF3are estimable with optimal average efficiency. Experimental settings involving more factor levels are also considered, tables are given showing the efficiency of the resulting deletion designs to compare favorably with optimal upper bounds, and the deletion designs are shown by comparison to be more efficient on lower-order effects than competing orthogonal designs.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478339

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A generalization of a locally most powerful unbiased (LMPU) test, for the single parameter case, to thek-parameter case is proposed. In particular, we define a locally most mean power unbiased (LMMPU) test based on the mean curvature of the power hypersurface. Compared with the type C tests (Neyman and Pearson 1938) and the type D tests, LMMPU tests possess better theoretical properties and enjoy ease of construction of critical regions in practical situations. LMMPU tests are obtained for the important practical case (Perng and Littel 1976) of a two-parameter univariate normal population, for which Isaacson (1951, p. 233) was unable to find a type D test, and for the case of means of a multivariate normal population with independent coordinates.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478340

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Suppose thatnhypothesesH1,H2, …,Hnwith associated test statisticsT1,T2, …,Tnare to be tested by a procedure withexperimentwise significance level(the probability of rejecting one or more true hypotheses) smaller than or equal to some specified value α. A commonly used procedure satisfying this condition is the Bonferroni (B) procedure, which consists of rejectingHi, for anyi, iff the associated test statisticTiis significant at the level α′ = α/n.Holm (1979) introduced a modified Bonferroni procedure with greater power than the B procedure. Under Holm's sequentially rejective Bonferroni (SRB) procedure, if any hypothesis is rejected at the level α′ = α/n, the denominator of α′ for the next test isn− 1, and the criterion continues to be modified in a stagewise manner, with the denominator of α′ reduced by 1 each time a hypothesis is rejected, so that tests can be conducted at successively higher significance levels. Holm proved that the experimentwise significance level of the SRB procedure is ≤ α, as is that of the original B procedure. Often, the hypotheses being tested are logically interrelated so that not all combinations of true and false hypotheses are possible. As a simple example of such a situation suppose, given samples from three distributions, we want to test the three hypotheses of pairwise equality: μi= μ′i(i<i′ = 1, 2, 3), where μiis the mean of distributioni.It is easily seen from the relations among the hypotheses that if any one of them is false, at least one other must be false. Thus there cannot be one false and two true hypotheses among these three. If we are testing all hypotheses of pairwise equality with more than three distributions, there are many such constraints. As another example, consider the hypotheses of independence of rows and columns of all 2×2 subtables of aKxLcontingency table. It is shown that if one such hypothesis is false, then at least (K− 1) (L− 1) must be false. When there are logical implications among the hypotheses and alternatives, as in the preceding examples, Holm's SRB procedure can be improved to obtain a further increase in power. This article considers methods for achieving such improvement. One way of modifying the SRB method is as follows: Given thatj− 1 hypotheses have been rejected, the denominator of α′, instead of being set atn−j+ 1 for the next test as in the SRB procedure, can be set attj, wheretjequals the maximum number of hypotheses that could be true, given that at leastj− 1 hypotheses are false. Obviously,tjis never greater thann−j+ 1, and for some values ofjit may be strictly smaller, as forj= 2 in the first example. Then this modified sequentially rejective Bonferroni (MSRB) procedure will never be less powerful (and typically will be more powerful) than the SRB procedure while (as is proved in the article) maintaining an experimentwise significance level ≤ α. The MSRB procedure is readily applicable to a wide variety of standard and nonstandard problems. A number of examples are given, and extensions and generalizations are discussed. It is pointed out that the methods may be adapted in some circumstances to the use of non-Bonferroni multiple test procedures.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478341

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Log-linear statistical models are used to characterize random graphs with general dependence structure and with Markov dependence. Sufficient statistics for Markov graphs are shown to be given by counts of various triangles and stars. In particular, we show under which assumptions the triad counts are sufficient statistics. We discuss inference methodology for some simple Markov graphs.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478342

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This article examines the accuracy of normal approximations to confidence limits for the binomial (n,p) parameterp.The method of getting “exact” values from anFtable is too slow for practical use and useless for largen.The two usual approximations have unsatisfactory accuracy both for smallnand asymptotically, and the simpler one lacks an invariance property of the confidence limit. Hall's (1982) approximation also lacks invariance and, even when symmetrized, has unsatisfactory accuracy. Pratt's (1968) approximation has excellent accuracy for alln.Inversion of a Molenaar (1973) normal approximation to the binomial gives better asymptotic accuracy than Pratt's approximation, but poor values for observations close ton.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478343

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Data: A Collection of Problems From Many Fields for the Student and Research Worker.D. F. Andrews and A. M. Herzberg New York: Springer-Verlag, 1985. xx + 442 pp. $39.00. Reviewed by Samprit Chatterjee

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478344

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This article has no abstract

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478306

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor